L-Tile Covering
Take a 4x4 or 8x8 board and remove any one square. Cover the rest exactly with L-shaped tiles of three squares. It always works, wherever the hole is, and the reason is in cutting the board into four.
L-tiles: 0 of 5
Tap one square to remove. Any square will do.
How to play
Choose a "Board size", then tap one square to remove. After that, tap three squares that form an L (three squares inside a 2x2) and the tile is placed. Tap a placed tile to take it off; Reset lets you choose another hole. "Hint" goes from the idea, to the way of splitting into four, to the next place for a tile. "Auto-solve" follows the method, repeating "split into four, put one L in the centre", and outlines the area it is working on in purple.
Learn more
On a square board whose side is a power of two, removing any single square leaves a region that L-shaped tiles of three squares can cover exactly. The reason is induction. In a 2x2, the three squares left are already an L. A board twice as big is cut into four squares. The hole is inside one of them, so put one L in the centre, touching the three parts that have no hole. Now all four parts are half-size boards with one square missing, and we already know how to cover those, so use the smaller method four times. The count works out too: 4^k minus 1 is divisible by 3 (for 8x8, 63 / 3 = 21 tiles). This site checks that the method works for every possible hole on 2x2, 4x4, 8x8 and 16x16 boards.